I have a series of data (more specific, they are coördinates of a package attached to the end of a mini level-luffing crane. The "flightpath" is linear and horizontal.)
Now when I plot the data:
Notice the labels on both the X and Y axis. If you would take orthonormal axes, one would not be able to see this is NOT a straight line. YET, when I perform linear regression, the coefficient of determination is only 0.2133. Isn't this impossible? Shouldn't it be something like 0.999?
Note that I performed the statistical analysis (bot regression and determination of the statistical parameters) via Excel and via Geogebra.
If this is a normal R squared, then perhaps one of you could answer the following:
The reason I need R squared, is because I need a quantitative parameter which shows me how 'well' the flight path approximates a straight line. I thought R squared was a good idea but apparently not because in my situation it does not show what is a good flight path and what is not. (For clarification, this is a near PERFECT flight path).
yes, i think i see why you are puzzled, and your reaction is very honest.
the thing about a correlation coefficient is that (as used here) it measures the extent to which one variable can predict the variation in the second variable. so you can see why it is not that high. it is scaled to take into account the standard deviation of the second variable, so even if the error was reduced by a factor of ten, the $R^2$ value would not change.
therefore your conclusion is absolutely correct, that this is not the appropriate measure of accuracy that you want. a better measure would be the standard deviation of the error divided by the length of the path.
however the correlation is not useless. as you can see the errors are not randomly distributed along the flight path, but rather form almost exactly one cycle of a sinusoidal-type fluctuation. this might direct the designer's attention to some factor in the situation whose unwanted interference could be reduced.